Algebra worksheet — GCSE Foundation

1.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

2.Which expression is equivalent to 2(x + 6)?

3.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

4.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

5.a = 3 and b = 5. Work out the value of a²b.

6.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

7.Which of these equations is equivalent to 5x − 2 = 3x + 8?

8.Expand 2(x + 12)

9.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

10.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

11.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.

12.Write down the gradient of the line with equation y = 6 + 4x.

13.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.

14.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

15.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.